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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 3, Pages 489–518
DOI: https://doi.org/10.4213/tvp5473 (Mi tvp5473) 		 
A Gibbs conditional theorem under extreme deviation

M. Biret, M. Broniatowski, Z. Cao

Laboratoire de probabilités, statistique et modélisation, Sorbonne Université, Paris, France
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DOI: https://doi.org/10.4213/tvp5473
Abstract: We explore some properties of the conditional distribution of an independently and identically distributed (i.i.d.) sample under large exceedances of its sum. Thresholds for the asymptotic independence of the summands are observed, in contrast with the classical case when the conditioning event is in the range of a large deviation. This paper is an extension of Broniatowski and Cao [Extremes, 17 (2014), pp. 305–336]. Tools include a new Edgeworth expansion adapted to specific triangular arrays, where the rows are generated by tilted distribution with diverging parameters, and some Abelian type results.
Keywords: Gibbs conditional principle, extreme deviation.
Received: 31.12.2020
Revised: 06.11.2021
Published: 22.07.2022
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 3, Pages 389–414
DOI: https://doi.org/10.1137/S0040585X97T991015
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Biret, M. Broniatowski, Z. Cao, “A Gibbs conditional theorem under extreme deviation”, Teor. Veroyatnost. i Primenen., 67:3 (2022), 489–518; Theory Probab. Appl., 67:3 (2022), 389–414
Citation in format AMSBIB
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\by M.~Biret, M.~Broniatowski, Z.~Cao
\paper A~Gibbs conditional theorem under extreme deviation
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 3
\pages 489--518
\mathnet{http://mi.mathnet.ru/tvp5473}
\crossref{https://doi.org/10.4213/tvp5473}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4506220}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 3
\pages 389--414
\crossref{https://doi.org/10.1137/S0040585X97T991015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85151967919}
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